Spiking frequency versus odorant concentration in olfactory
receptor neurons
Jean-Pierre Rospars
a,*, Petr La´nsky´
b, Patricia Duchamp-Viret
c,
Andre´ Duchamp
caUnite´ de Biome´trie,INRA,78352Jouy-en-Josas,Versailles,Cedex,France bInstitute of Physiology,Academy of Sciences,CZ-142 20Prague4,Czech Republic cNeurosciences et Syste`mes sensoriels,Uni6ersite´ Claude Bernard,F-69622Villeurbanne Cedex,France
Abstract
The spiking response of receptor neurons to various odorants has been analyzed at different concentrations. The interspike intervals were measured extracellularly before, during and after the stimulation from the olfactory epithelium of the frog Rana ridibunda. First, a quantitative method was developed to distinguish the spikes in the response from the spontaneous activity. Then, the response intensity, characterized by its median instantaneous frequency, was determined. Finally, based on statistical analyses, this characteristic was related to the concentration and quality of the odorant stimulus. It was found that the olfactory neuron is characterized by a low modulation in frequency and a short range of discriminated intensities. The significance of the results is discussed from both a biological and a modelling point of view. © 2000 Elsevier Science Ireland Ltd. All rights reserved.
Keywords:Intensity coding; Interspike interval; Olfaction; Transduction; Neuron modeling
www.elsevier.com/locate/biosystems
1. Introduction
Intensity coding is a major aspect of sensory processes and the most amenable to quantitative analysis. It is widely believed that a frequency code is used by receptor cells to encode stimulus intensity (e.g. Shepherd, 1988; Duchamp-Viret and Duchamp, 1997; Hildebrand and Shepherd, 1997). In order to investigate the nature of the frequency code and its role in quality discrimination, one has
begun to analyze the trains of action potentials recorded from olfactory receptor neurons (ORNs) in response to various odorants at different concen-trations. A series of concentration – response curves were described quantitatively and were compared for different odorants. Four main questions were addressed. How can the response frequency be measured reliably in a noisy background? What are the average quantitative characteristics of the re-sponse curves in magnitude and sensitivity? What is the variability of these characteristics among neurons and odorants? Is it possible to account for these results in the framework of the ORN model proposed (Rospars et al., 1996)?
* Corresponding author. Present address: Unite de Phy-topharmacie et Mediateurs chimiques, INRA, 78026 Versailles Cedex, France. Fax: +33-1-30833359.
E-mail address:[email protected] (J.-P. Rospars).
2. Methods
2.1. Recordings
Spiking activity was recorded extracellularly from the olfactory epithelium of the frog Rana ridibunda and the interspike intervals (ISIs) were measured 30 s before and 30 s after the onset of 2-s stimulations (Fig. 1). The four odorants tested were anisole (ANI), DL-camphor (CAM), isoamyle acetate (ISO) and DL-limonene (LIM). They are representative of previously identified odorant groups, ANI for aromatic, CAM for camphoraceous and LIM for terpenic, except ISO which is not representative of any group (see Duchamp-Viret and Duchamp, 1997). The odor-ants were delivered as almost square pulses at precisely controled concentrations along a discrete scale determined by the stimulating apparatus. Due to the very large range of stimulus intensity used, a logarithmic measureCof the intensity was used, C=log(L), where L, expressed in mol/l, is the number of molecules of odorants per unit volume of odorized air delivered to the prepara-tion. A total of 550 stimulations of 40 ORNs were recorded.
2.2. Response detection
A two-step quantitative method was developed to distinguish the ISIs in the response from the spontaneous spikes. For each spike, the instanta-neous firing frequency Fi was determined as the
inverse of the interspike interval xi. The response
was defined as the first uninterrupted series of at least three ISIs having Fi higher than a given
threshold Fu and significantly shorter than the spontaneous ISIs as judged by a Mann and Whit-ney test (Conover, 1980).Fuwas chosen 1.5 spike/ s above the median of the spontaneous firing frequency of the neuron studied (the spontaneous ISIs being distributed asymmetrically between 0 and 3.85 spike/s with median 1.15 spike/s; Rospars et al., 1994). A total of 350 significant responses were found. Each response was charac-terized by its median firing frequency F. The curvesFversusCwere plotted for a given neuron stimulated by a single odorant at different concen-trations (Fig. 2). The plots with only one or two responses were discarded. One was left for statisti-cal analyses with 57 curves including 335 responses.
Fig. 2. Concentration – response curve with logistic (black line) and arc tangent (grey line) fittings. Same example as in Fig. 1. Response properties (maximum firing frequencyFM, threshold
Ct, saturationCs, and dynamic rangeDC) are indicated for the logistic curve.
zero frequency; in the case of logistic the same was done for all concentrations up to and includ-ing C0. As in a previous modelling work (e.g.
Rospars et al., 1996), these calculated parameters were not used directly but converted to more meaningful characteristics, the maximum response
FM (horizontal asymptote), the logconcentrations
at thresholdCtand close to saturationCs, and the
dynamic range DC=Cs−Ct giving the ratio in
log units of the extreme concentrations (see Fig. 2).
3. Results
3.1. Global characteristics of responses and cur6es
Pooling all odorants and concentrations to-gether, the firing frequency F is found to lay in the range 2.9 – 26.3 with a mean of 9.2 spike/s. This shows that even the strongest responses are relatively weak. Two-way analysis of variance shows that the response frequency cannot be pre-dicted from the knowledge of the odorant type alone, which means that all odorants act on fre-quency in the same way. The knowledge of the neuron alone is more informative and still more that of both the neuron and the odorant.
The weakest stimulus C eliciting a response is
−11, the strongest −4.9, and the median strength being −6.7. These values depend on the odorant. CAM appears as the most effective odorant, ISO the least efficient one, with LIM and ANI of similar intermediate efficiencies. Interest-ingly, this ordering is consistent with that based on the proportion of significant responses with respect to the total number of stimulations, CAM giving the highest proportion (81%) and ISO the lowest (65%).
Plots of the response frequencyFas a function of log concentration C showed that most of the plots were monotonically increasing. However, some curves (in at most four neurons) were an exception to this rule. They showed with some odorants a long plateau at relatively low firing frequency (ca. 7 spike/s) starting at low concen-tration followed in two cases with a terminal increase culminating at ca. 20 spike/s. In these 2.3. Cur6e fitting
The C–F curves were fitted to 3-parameter logistic and arc tangent functions (Fig. 2). The logistic function is
F(C)= a
1+exp(−b(C−d)). (1)
where a\0,b\0 and d are the parameters esti-mated from the data. It possesses two asymptotes, the lower one is zero when Cdecreases and the upper one is a when C increases to infinity. The arc tangent function is
F(C)=2a
p a tan(b(C−g)), forC\g. (2)
where a\0, b\0 and g are the estimated parameters. It possesses one asymptote alpha when C tends to infinity. Parameters a and a
characterize the maximum response of the neu-ron. In most cases (96% of logistic and 86% of arc tangent) the three parameters of the fitted curves were obtained using a nonlinear least-square al-gorithm. A generalization of (1) introducing an exponent (Hill coefficient) greater than one has not been used because determining a fourth parameter was usually not feasible due to the number of points available. In the case of arc tangent fits, the first deliverable concentration C0
three cases only the part of the curve corresponding to the initial plateau was kept for fitting.
3.2. Maximum firing frequency (Fig. 3)
The asymptotic frequency a predicted by the logistic fit (13.598.1 spike/s, median 11.5) is slightly smaller than that a predicted by the arc tangent fit (15.5910.1 spike/s, median 13). The predictions are conservative; only in rare cases they suggest that the true maximum might be above the maximum observed experimentally. The median values ofa,aand the maximum observed frequency are all in the range 11 – 13 spike/s. The distributions of these parameters are asymmetrical (Fig. 3) and the hypothesis of a normal distribution is rejected for both a and a. This global behavior masks differences between odorants. Whatever the parametera ora considered, CAM produced the
strongest maximum responses (median 14 – 19 spike/s) and LIM the weakest (median 7 – 8 spike/s), whereas ANI and ISO are barely distinguishable (median 11 – 15 spike/s), see Fig. 4a.
3.3. Concentration at threshold (Fig. 5)
For all neurons and odorants pooled together, the logconcentration C0.05 at which the logistic
curves reach 5% of their maximum varies between
−11.5 and −5.5, with a median at −7.8. This is very similar to the range of concentrations C0
(−11.2 to −5.6) at which the arc tangent curves rise from 0. For both curves the histograms are remarkably uniform (Fig. 5). Part of the variability between curves comes from differences between odorants (Fig. 4b), the curve corresponding to CAM being shifted to the left (median threshold is at C0.05#C0#−8.6) with respect to the other
odorants (−6.7 ISO, −7.0 ANI, −7.7 LIM). Analysis of variance shows that ISO and CAM are significantly different.
3.4. Concentration close to maximum response
(Fig. 6)
The approach to the asymptote is quantified by the logconcentration C0.95 and C0.80 giving 95%
(logistic) and 80% (arc tangent) of the maximum response. These values vary between−9.5 and−3 with a median at −7.0 for the logistic curves and between −9.1 and −3.3 with a median at −6.9 for the arc tangent curves. These estimates are in good agreement. The histograms are asymmetric with modes greater than the medians (Fig. 6). Here again CAM curves are shifted to the left with respect to ANI, ISO and LIM (Fig. 4c). The median saturation moves approximately from −7.0 for CAM and −6.2 for LIM, to −5.3 for ANI and ISO. The odorants do not form an homogeneous group and CAM is significantly different from ANI for both logistic and arc tangent.
3.5. Dynamic range (Fig. 7)
The range of concentrations (DC) over which the response frequency increases from 5 to 95% in Fig. 3. Maximum frequency (in spike/s). Histograms for
Fig. 4. Odors have different response characteristics. Comparison of cumulative frequencies forFm,Ct,CsandDC(see Fig. 2) for CAM, ANI, ISO and LIM.
logistic curves varies from 0.2 to 3.9 (rejecting four outliers) log units depending on neurons and odorants. The distribution of DC is very asymmetric with a median at 1.0 log unit (Fig. 7). With arc tangent curves, and a response interval going from 0 to 80%, the dynamic range lays principally in the interval 0.1 to 4 log units (rejecting two outliers) with median 1.0. It has been seen above that CAM curves are in general shifted to the left. This shift is uniform because it has the same dynamic range as the other three odorants. Whatever the odorant the median dynamic range is about 0.3 – 1.2 (logistic) and 0.7 – 1.4 log units (arc tangent). Therefore the estimates of DeltaCdo not depend on the model curve (which is expected) and are also remarkably independent of the odorant considered (Fig. 4d).
3.6. Correlation between characteristics(Fig. 8)
The correlations between Ct and FM, and Ct
andDCare low, which means that a high sensiv-ity response curve can have a low or a high
maximum frequency and a narrow or wide dy-namic range.
4. Discussion
4.1. Methodological aspects
constraint must be taken into account in inter-preting the results because it implies that the smallest frequencies one was able to detect are probably relatively large with respect to the smallest actual responses, that may be effective at the olfactory bulb level. Clearly, the sensory threshold was not directly measurable. If, for example, the logconcentration at thresholdC0.1 is
defined as the intensity giving a frequencyF0.1of,
for example, 10% of the maximum frequency, then the median value of this inferior limit is 1.3 spike/s, which is half the median value of the detection threshold Fu that was actually used (2.65 spike/s). This limitation, however, does not necessarily affect the estimation of the sensory threshold Cs and dynamic range, because Cs was
estimated indirectly from the fitted curves at 5 (logistic) or 0% (arc tangent) of FM, and not
directly from the measurable responses.
Fig. 6. Concentration at saturation (in log mol/l). Same pre-sentation as in Fig. 3.
Fig. 5. Concentration at threshold (in log mol/l). Same presen-tation as in Fig. 3.
4.2. Properties of F–C cur6es
4.2.1. Typical response cur6e
The typical (median) neuron starts to fire at aboutCt= −7.5, i.e. 10
−7.5mol/l, and reaches its
maximum firing rate of about 12 spikes/s atCs=
−6.5, which corresponds to a dynamic range of ca. 1 log unit, i.e. the highest discriminated con-centration is only about 10 times larger than the smallest one. So, the typical ORN in this frog species is characterized by a low modulation in frequency and a short range of discriminated in-tensities. This suggests that coding of a wide range of concentrations cannot be achieved by any single neuron but involves a whole population of neurons, each neuron responding in a different segment of the complete range, although confir-mation of this statement must wait for the analy-sis of the other features of the responses (such as latency and duration, see Fig. 1).
Fig. 8. Correlation of response characteristics.
Fig. 7. Dynamic range (in log mol/l). Same presentation as in Fig. 3.
4.2.2. Di6ersity of cur6es
However, this standard behavior can be modu-lated by the variations of all four characteristics. The range of variation of the maximum firing rate, threshold, saturation point, and dynamic range are 55FM530 spike/s, 9.55Ct5−5.5,
−9.55Cs5−3, and 0.15DC54, respectively.
So, all characteristics except DC, remain approxi-mately in an interval comprised between half and twice their median value. It follows from the weak correlations between characteristics (Fig. 8), espe-cially ofCtwithFMandDC, that these
4.2.3. Comparison of odorants (quality coding) Responses to CAM in most neurons are sys-tematically stronger and more sensitive than that to the other three odorants (Fig. 4). However, the dynamic range does not seem to be modified and remains close to the global median (Fig. 4d). Conversely, the least stimulating odorants are ISO for threshold (sensitivity) and LIM for maximum firing (magnitude).
4.3. Comparison with a model neuron
The spiking response curves can be fitted to the steady-state model of the olfactory receptor neuron developed (Rospars et al., 1996, see also La´nsky´ and Rospars, 1993, 1998; Vermeulen and Rospars, 1998). This model can readily ac-count for the diversity of the observed curves in magnitude (along the F-axis) and sensitivity (along the C-axis). Assuming that after a 2-s stimulation the receptor has reached a steady state, the F–C curves can be described by only four constants, the dissociation K1 and
deactiva-tion K2 equilibrium constants which characterize
respectively the binding of the odorant to the receptor and the subsequent activation step, the ratio gmax/gm of the maximum conductance gmax
of the sensory membrane to its resting conduc-tance gm and the ratio S/E of the spiking
threshold S (in mV) to the equilibrium potential
E of permeating ions at the sensory membrane. According to this model gmax/gm must remain
between 1 and 10 and S/E between 0.01 and 0.05 in order to get the observed maximum firing frequency of 12 spike/s. Then, assuming
K2 is close to 1 (Minor et al., 1999; Rospars et
al., 2000), K1 must be ca. 10−5 mol/l in order
to get the average concentration threshold of 10−7.5
mol/l. The estimate of gmax/gm indicates
that at maximum neuron response the number of activated receptors is likely much smaller than the total number of available receptors. The model suggests that most of the variability in neuron sensitivity is accounted for by the variability of receptor affinities for odorant, as measured by K1. Finally, it suggests that CAM,
for example, can interact more easily (smaller
K1) with more receptor types and consequently
with more types of neurons (higher proportion of responding neurons) than the other odorants. Both aspects could result from the small size and round shape of this molecule (Eminet and Chastrette, 1983).
Acknowledgements
This work was partly supported by NATO Collaborative Linkage Grant LST.CLG.976786, by joint cooperation project Barrande No. 972 SL between France and the Czech Republic, by grant from De´partement Sante´ des Plantes et Environnement of INRA, and by Grant Agency of the Czech Academy of Sciences (Grant No. A7011712).
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